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Math Help - Explaining Similar Triangles

  1. #1
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    Explaining Similar Triangles

    Hi
    Is anybody able to put this in words for me?
    (Why the pink and yellow triangles are similar)

    Thanks
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  2. #2
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    Lexington, MA (USA)
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    Hello, 200001

    Is anybody able to put this in words for me?
    (Why the two shaded triangles are similar.)
    Code:
        A * - - - - - - - - - - - - - - - * F
          |*  *                           |
          |:*     *                       |
          |::*        *                   |
          | β *           *               |
          |::::*              *           |
          |:::::*                 *       |
          |::::::* 9                  *   | 
          |:::::::*                       * E
          |::::::::*                   *::|
          |:::::::::*            3  *: α :|
          |::::::::::*           *::::::::|
          |:::::::::::*  90  *:::::::::::|
          |:::::::: α :*   *: β ::::::::::|
        B * - - - - - - * - - - - - - - - * D
                        C

    In right triangle ABC, let  \alpha \,=\,\angle ACB

    Then \beta \,=\,\angle CAB is the complement of \alpha\!:\;\;\beta \:=\:90^o - \alpha


    At point C, we have: . \alpha + 90^o + \angle ECD \:=\:180^o \quad\Rightarrow\quad \angle ECD \:=\:90^o - \alpha

    . . Hence: . \angle ECD \,=\,\beta

    In right triangle CDE,\; \angle CED is the complement of \angle ECD\:(\beta)

    . . Hence: . \angle CED = \alpha


    Therefore: . \Delta ABC \sim \Delta CDE\;\;(a.a.a)

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  3. #3
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    Awesome...thats perfect.
    Thanks
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